The Physics volume of the DUNE far detector (FD) Technical Design Report (TDR) presents the science program of DUNE. Within, we describe the array of identified scientific opportunities and key goals. Crucially, we also report our best current understanding of the capability of DUNE to realize these goals, along with the detailed arguments and investigations on which this understanding is based. In the context of the complete set of DUNE TDR volumes, a central role for this volume is to document the scientific basis underlying the conception and design of the LBNF/DUNE experimental configurations. As a result, it is the description of DUNE's experimental capabilities that constitutes the bulk of the document. Key linkages between requirements for successful execution of the physics program and primary specifications of the experimental configurations are drawn and summarized. This document also serves a wider purpose as a statement on the scientific potential of DUNE as a central component within a global program of frontier theoretical and experimental particle physics research. Thus, the presentation also aims to serve as a resource for the particle physics community at large. In this chapter, the scientific goals, the methodologies utilized to obtain sensitivity projections, the corresponding results for selected elements of the scientific program, and the demands placed on the experiment design and performance are presented in summary form. Together with the two chapters that follow, this summary establishes the context for the detailed descriptions specific to each area of research that comprise the remaining chapters.